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1

DULGARIAN, ROBERT. "Richard Baxter, Thomas Barlow and the Advice to a Young Student in Theology, St John's College, Cambridge, MS K.38: A Preliminary Assessment." Journal of Ecclesiastical History 69, no. 2 (2017): 345–66. http://dx.doi.org/10.1017/s0022046917000689.

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This article identifies as the work of Richard Baxter a set of ecclesiastical directions and reading recommendations contained in fos 180–208 of St John's College, Cambridge, MS K.38, once tentatively ascribed to Thomas Barlow, but demonstrably a close analogue of British Library, MS Harleian 6009, which is a copy of a lost Baxter original. Internal evidence of MS K.38 and comparison with MS 6009 and Baxter's Christian directory imply both an earlier date and a wider circulation of Baxter's archetype than hitherto suspected, suggesting a new direction of inquiry into Baxter's scholarly and ecclesiastical associations.
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2

Bouvel, Mathilde, Veronica Guerrini, Andrew Rechnitzer, and Simone Rinaldi. "Semi-Baxter and Strong-Baxter: Two Relatives of the Baxter Sequence." SIAM Journal on Discrete Mathematics 32, no. 4 (2018): 2795–819. http://dx.doi.org/10.1137/17m1126734.

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3

Bäccman, Charlotte, Per Folkesson, and Torsten Norlander. "EXPECTATIONS OF ROMANTIC RELATIONSHIPS: A COMPARISON BETWEEN HOMOSEXUAL AND HETEROSEXUAL MEN WITH REGARD TO BAXTER'S CRITERIA." Social Behavior and Personality: an international journal 27, no. 4 (1999): 363–74. http://dx.doi.org/10.2224/sbp.1999.27.4.363.

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According to Baxter (1986) every relationship has rules which must be followed. If at least one of these rules is broken, it gives the individual the right to breakup the relationship. Baxter identified eight such rules or criteria. The aim of the present study was to investigate whether or not the expectations of romantic relationships held by homosexual men can be linked to Baxter's criteria. Data were obtained through a questionnaire addressed to 31 homosexual men and 50 heterosexual men. Results indicated that Baxter's criteria can be linked to expectations of romantic relationships held by men regardless of sexual orientation, and that age and experience are more reliable predictors than is sexual orientation.
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4

CONDIE, KEITH. "SOME FURTHER CORRESPONDENCE BETWEEN RICHARD BAXTER AND KATHERINE GELL." Historical Journal 53, no. 1 (2010): 165–76. http://dx.doi.org/10.1017/s0018246x0999046x.

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ABSTRACTThe puritan pastor and writer, Richard Baxter, and a member of a prominent Derbyshire family, Katherine Gell, exchanged a series of letters between 1655 and 1658. This article highlights the existence of three further items of correspondence in this exchange, located in the Derbyshire Record Office, hitherto believed not to be extant. The additional three letters are all penned by Baxter and include his replies to her first two epistles (dated 28 July 1655 and 4 September 1655) as well as a reply to a non-extant Gell letter (dated 31 July 1658). The correspondence provides valuable insights into Baxter's pastoral methods and the nature of puritan piety. The first two items draw attention to the importance of the dimension of duty within Baxter's pastoral agenda; while expressed in a context of warmth and encouragement, he believes that Gell will find a measure of resolution to her spiritual struggles by careful attention to the obligations of Christian living. The third letter, written some years later, after Baxter has discovered that Gell suffers from melancholia, is couched in a gentler tone and reveals a more reciprocal dimension to their relationship.
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5

Horling, Frank M., Christine Lenk, Rafi Uddin Ahmad, et al. "Preclinical Immunogenicity Assessment of Baxter‘s Recombinant Factor VIIa,." Blood 118, no. 21 (2011): 3327. http://dx.doi.org/10.1182/blood.v118.21.3327.3327.

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Abstract Abstract 3327 Baxter has developed a recombinant FVIIa (rFVIIa) product for the treatment of hemophilia patients with factor VIII or factor IX inhibitors. Before entering clinical development we assessed the immunogenic safety profile of the new product candidate BAX 817 using two novel mouse models that mimicked specific aspects of the situation in patients. Several comparative preclinical immunogenicity studies were conducted to assess the immunogenicity profile of Baxter`s rFVIIa BAX 817 in comparison to a licensed recombinant FVIIa product. Three different mouse models were used for this purpose. The first model expresses specific immune tolerance against human FVIIa and, therefore, mimics the situation in both hemophilia A and hemophilia B patients. Using this model, we asked if Baxter‘s rFVIIa is able to maintain immune tolerance to human FVIIa. The second model is a hemophilia A model that mimics the situation in an important fraction of hemophilia A patients with FVIII inhibitors. This model expresses a human MHC-class II haplotype (HLA-DRB1*1501) that was previously shown to be associated with an increased risk for the development of FVIII inhibitors. The third model represents a normal wildtype C57BL/6 mouse. All mice were treated with 8 weekly doses of either Baxter‘s rFVIIa BAX 817 or a licensed recombinant FVIIa product. Total anti-FVIIa antibodies were analyzed prior to the first dose as well as after the 4th and the 8th dose using ELISA assays. Baxter`s rFVIIa BAX 817 and a licensed recombinant FVIIa product induced similar titers of anti-FVIIa antibodies in C57BL/6 wildtype mice and in hemophilic HLA-DRB1*1501 mice. In addition, both Baxter`s rFVIIa BAX 817 and a licensed recombinant FVIIa product were able to maintain specific immune tolerance in a novel mouse model that is immunologically tolerant to human FVIIa. Based on the data obtained we conclude that both Baxter‘s rFVIIa BAX 817 and a licensed recombinant FVIIa product have a comparable immunogenic safety profile. Disclosures: Horling: Baxter Innovations GmbH: Employment. Lenk:Baxter BioScience: Employment. Ahmad:Baxter BioScience: Employment. Weiller:Baxter BioScience: Employment. Schuster:Baxter Innovation GmbH: Employment. Schwarz:Baxter Innovations GmbH: Employment. Reipert:Baxter Innovations GmbH: Employment.
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6

GUO, LI. "ASCENDING CHAIN CONDITIONS IN FREE BAXTER ALGEBRAS." International Journal of Algebra and Computation 12, no. 04 (2002): 601–22. http://dx.doi.org/10.1142/s0218196702001152.

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In this paper we study ascending chain conditions in a free Baxter algebra by making use of explicit constructions of free Baxter algebras that were obtained recently. We investigate ascending chain conditions both for ideals and for Baxter ideals. The free Baxter algebras under consideration include free Baxter algebras on sets and free Baxter algebras on algebras. We also consider complete free Baxter algebras.
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7

Ma, Tianshui, and Linlin Liu. "Rota–Baxter coalgebras and Rota–Baxter bialgebras." Linear and Multilinear Algebra 64, no. 5 (2015): 968–79. http://dx.doi.org/10.1080/03081087.2015.1068269.

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8

Zhang, Yi, and Shuangjian Guo. "Matching Rota-Baxter Systems and Gröbner-Shirshov Bases." Algebra Colloquium 31, no. 03 (2024): 389–406. http://dx.doi.org/10.1142/s1005386724000294.

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Motivated by the concept of matching Rota-Baxter algebras arising from polarized associative Yang-Baxter equations and Volterra integral equations, we introduce the notion of a matching Rota-Baxter system, which generalizes the Rota-Baxter system proposed by Brzeziński. We show that this notion is also related to Yang-Baxter pairs and to matching pre-Lie algebras. We then modify the definition of matching Rota-Baxter systems by adding a curvature term, and make a connection with matching pre-Lie algebras and with compatible associative algebras. Furthermore, we study matching Rota-Baxter systems on a dendriform algebra and show how they induce matching quadri-algebra structures. Finally, we give a linear basis of free matching Rota-Baxter system by Gröbner-Shirshov bases methods.
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9

Zhu, Fuyang, and Wen Teng. "Cohomology and Crossed Modules of Modified Rota–Baxter Pre-Lie Algebras." Mathematics 12, no. 14 (2024): 2260. http://dx.doi.org/10.3390/math12142260.

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The goal of the present paper is to provide a cohomology theory and crossed modules of modified Rota–Baxter pre-Lie algebras. We introduce the notion of a modified Rota–Baxter pre-Lie algebra and its bimodule. We define a cohomology of modified Rota–Baxter pre-Lie algebras with coefficients in a suitable bimodule. Furthermore, we study the infinitesimal deformations and abelian extensions of modified Rota–Baxter pre-Lie algebras and relate them with the second cohomology groups. Finally, we investigate skeletal and strict modified Rota–Baxter pre-Lie 2-algebras. We show that skeletal modified Rota–Baxter pre-Lie 2-algebras can be classified into the third cohomology group, and strict modified Rota–Baxter pre-Lie 2-algebras are equivalent to the crossed modules of modified Rota–Baxter pre-Lie algebras.
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10

Adams, Anthony P. "FRED BAXTER." Survey of Anesthesiology 41, no. 6 (1997): 327. http://dx.doi.org/10.1097/00132586-199712000-00014.

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11

Dulucq, S., and O. Guibert. "Baxter permutations." Discrete Mathematics 180, no. 1-3 (1998): 143–56. http://dx.doi.org/10.1016/s0012-365x(97)00112-x.

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12

Baxter, Gordon. "Gordon Baxter." Interactions 27, no. 1 (2019): 15. http://dx.doi.org/10.1145/3374233.

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13

Neachell, Emma, and Geoff Petts. "George Baxter." Progress in Physical Geography: Earth and Environment 41, no. 5 (2017): 686–97. http://dx.doi.org/10.1177/0309133317732922.

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This paper summarizes the innovative approach to setting environmental flows proposed by Baxter in 1961, describes its immediate impact across both engineering and fisheries disciplines and explores the reasons why his approach was not adopted in river flow regulation and management in the UK. Yet, the basic approach was to be used world-wide by the end of the century. Several barriers constrained innovation in flow regulation in England during the 1960s: the overwhelming pollution problems; serious concerns about water shortage and food security, not least in the context of the severe 1959 drought; the influence of the 1963 Water Resources Act and the legacy of previous legislation; the limited availability of both river flow data and biological data; and the lack of awareness of human impacts on the environment. The paper also provides lessons for promoting environmental science into policy and practice to advance the implementation of environmental flows.
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14

EBRAHIMI-FARD, KURUSCH, and LI GUO. "FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES." Journal of Algebra and Its Applications 07, no. 02 (2008): 167–94. http://dx.doi.org/10.1142/s0219498808002746.

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A Rota–Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota–Baxter relation, that generalizes the integration by parts formula. Most of the studies on Rota–Baxter algebras have been for commutative algebras. Two constructions of free commutative Rota–Baxter algebras were obtained by Rota and Cartier in the 1970s and a third one by Keigher and one of the authors in the 1990s in terms of mixable shuffles. Recently, noncommutative Rota–Baxter algebras have appeared both in physics in connection with the work of Connes and Kreimer on renormalization in perturbative quantum field theory, and in mathematics related to the work of Loday and Ronco on dendriform dialgebras and trialgebras. This paper uses rooted trees and forests to give explicit constructions of free noncommutative Rota–Baxter algebras on modules and sets. This highlights the combinatorial nature of Rota–Baxter algebras and facilitates their further study. As an application, we obtain the unitarization of Rota–Baxter algebras.
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15

Chen, Dan, Yan-Feng Luo, Yi Zhang та Yuan-Yuan Zhang. "Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases". International Journal of Algebra and Computation 30, № 07 (2020): 1359–73. http://dx.doi.org/10.1142/s0218196720500447.

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Motivated by the formula of partial integration, we introduce the concept of [Formula: see text]-Rota–Baxter algebras, which generalizes the Rota–Baxter algebras introduced by Baxter. We then construct free objects in the category of [Formula: see text]-Rota–Baxter algebras, via a method of Gröbner–Shirshov bases.
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16

Zhang, Liangyun, Linhan Li, and Huihui Zheng. "Rota-Baxter Leibniz Algebras and Their Constructions." Advances in Mathematical Physics 2018 (December 2, 2018): 1–15. http://dx.doi.org/10.1155/2018/8540674.

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In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota-Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra. In the end, we give all Rota-Baxter operators of weight 0 and -1 on solvable and nilpotent Leibniz algebras of dimension ≤3, respectively.
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17

Wang, Ximu, Chongxia Zhang, and Liangyun Zhang. "Rota–Baxter Operators on Skew Braces." Mathematics 12, no. 11 (2024): 1671. http://dx.doi.org/10.3390/math12111671.

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In this paper, we introduce the concept of Rota–Baxter skew braces, and provide classifications of Rota–Baxter operators on various skew braces, such as (Z,+,∘) and (Z/(4),+,∘). We also present a necessary and sufficient condition for a skew brace to be a co-inverse skew brace. Additionally, we describe some constructions of Rota–Baxter quasiskew braces, and demonstrate that every Rota–Baxter skew brace can induce a quasigroup and a Rota–Baxter quasiskew brace.
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18

Novak, Michael. "Liberal Ideology, An Eternal No; Liberal Institutions, A Temporal Yes? And Further Questions." Review of Politics 60, no. 4 (1998): 765–74. http://dx.doi.org/10.1017/s0034670500050889.

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Michael Baxter's long review provides an outline of David Schindler's useful first book; concentrates on its treatment of John Courtney Murray; gives a free pass to its lengthy ontological and theological speculations; and calls attention to its impracticality. Like Baxter, I share de Lubac's view of grace and nature (mediated to me by three Jesuits, Henry Bouillard, Juan Alfaro, and Bernard Lonergan), although I draw from it practical applications quite different from those of Schindler and Baxter. Further, I agree with the main thrust of Baxter's criticism: just where one wants to test Schindler's grand hypotheses about how grace ought to work in a “civilization of love,” particularly with regard to politics and economics, Schindler has almost nothing practical to say, and such few gestures as he offers seem lamely indistinguishable from those he criticizes, for example Murray (on the First Amendment) and Richard John Neuhaus (on the public square). His reading of my own work, too, is excessively polemical.
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19

BAI, CHENGMING, LI GUO, and XIANG NI. "RELATIVE ROTA–BAXTER OPERATORS AND TRIDENDRIFORM ALGEBRAS." Journal of Algebra and Its Applications 12, no. 07 (2013): 1350027. http://dx.doi.org/10.1142/s0219498813500278.

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A relative Rota–Baxter operator is a relative generalization of a Rota–Baxter operator on an associative algebra. In the Lie algebra context, it is called an [Formula: see text]-operator, originated from the operator form of the classical Yang–Baxter equation. We generalize the well-known construction of dendriform and tridendriform algebras from Rota–Baxter algebras to a construction from relative Rota–Baxter operators. In fact we give two such generalizations, on the domain and range of the operator respectively. We show that each of these generalized constructions recovers all dendriform and tridendriform algebras. Furthermore the construction on the range induces bijections between certain equivalence classes of invertible relative Rota–Baxter operators and tridendriform algebras.
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20

Schindler, David L. "Communio Ecclesiology and Liberalism." Review of Politics 60, no. 4 (1998): 775–86. http://dx.doi.org/10.1017/s0034670500050890.

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I. I begin with a discussion of Father Michael Baxter's reflections on my Heart of the World, Center of the Church (HWCC). I am deeply grateful for the evident care and thoroughness with which he read the book, and can suggest here only the beginning of a reply to his serious questions.Appropriately for the audience of the Review of Politics, Baxter develops his reflections mostly in terms of my argument regarding John Courtney Murray. Granting a basic validity to my critique of Murray, Baxter nonetheless argues that, in the end, my own constructive proposal “gets vague,” and he suspects that “it will turn out not to be substantially different from what has already been proposed by Murray and his successors.”
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21

Black, J. William. "From Martin Bucer to Richard Baxter: “Discipline” and Reformation in Sixteenthand Seventeenth-Century England." Church History 70, no. 4 (2001): 644–73. http://dx.doi.org/10.2307/3654544.

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Already famous for his best-selling books on Christian devotion and increasingly infamous for his attempts at a theological synthesis of Calvinist and Arminian perspectives on salvation—which (no surprise) pleased hardly anyone—Richard Baxter (1615–91) nearly succeeded in redefining English pastoral practice before the Restoration brought his experiment in pastor-led, parish-based reformation to a frustrating end. At the core of his efforts to bring reformation to Kidderminster lay his efforts to establish a parish-based system of church discipline that would preserve the integrity of the sacraments and thus rob separatists of one of their primary excuses for abandoning the parochial system. This article seeks to place Baxter's effort to develop a strategy for an effective church discipline in its historical context. In particular, I will first consider the precedents to the system which Richard Baxter developed for St. Mary's parish. Special attention will be given to Martin Bucer's Reformation-era prescription for reforming the discipline of the church and the intriguing possibility that Baxter's strategy was actually a recovery of Bucerian pastoral emphases. Second, I will trace the evolution of Baxter's own program for discipline. Finally, I will discuss the impact Baxter's discipline had on his wider goal of reformation, both in his parish and beyond.
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22

Liu, Ling, Abdenacer Makhlouf, Claudia Menini, and Florin Panaite. "-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation." Canadian Mathematical Bulletin 62, no. 02 (2019): 355–72. http://dx.doi.org/10.4153/cmb-2018-028-8.

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AbstractWe introduce the concept of a $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$ -Rota–Baxter operator, as a twisted version of a Rota–Baxter operator of weight zero. We show how to obtain a certain $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$ -Rota–Baxter operator from a solution of the associative (Bi)Hom-Yang–Baxter equation, and, in a compatible way, a Hom-pre-Lie algebra from an infinitesimal Hom-bialgebra.
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23

Dimakis, Aristophanes, and Folkert Müller-Hoissen. "Tropical limit of matrix solitons and entwining Yang–Baxter maps." Letters in Mathematical Physics 110, no. 11 (2020): 3015–51. http://dx.doi.org/10.1007/s11005-020-01322-9.

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Abstract We consider a matrix refactorization problem, i.e., a “Lax representation,” for the Yang–Baxter map that originated as the map of polarizations from the “pure” 2-soliton solution of a matrix KP equation. Using the Lax matrix and its inverse, a related refactorization problem determines another map, which is not a solution of the Yang–Baxter equation, but satisfies a mixed version of the Yang–Baxter equation together with the Yang–Baxter map. Such maps have been called “entwining Yang–Baxter maps” in recent work. In fact, the map of polarizations obtained from a pure 2-soliton solution of a matrix KP equation, and already for the matrix KdV reduction, is not in general a Yang–Baxter map, but it is described by one of the two maps or their inverses. We clarify why the weaker version of the Yang–Baxter equation holds, by exploring the pure 3-soliton solution in the “tropical limit,” where the 3-soliton interaction decomposes into 2-soliton interactions. Here, this is elaborated for pure soliton solutions, generated via a binary Darboux transformation, of matrix generalizations of the two-dimensional Toda lattice equation, where we meet the same entwining Yang–Baxter maps as in the KP case, indicating a kind of universality.
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24

Das, Apurba, and Satyendra Kumar Mishra. "The L∞-deformations of associative Rota–Baxter algebras and homotopy Rota–Baxter operators." Journal of Mathematical Physics 63, no. 5 (2022): 051703. http://dx.doi.org/10.1063/5.0076566.

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A relative Rota–Baxter algebra is a triple ( A, M, T) consisting of an algebra A, an A-bimodule M, and a relative Rota–Baxter operator T. Using Voronov’s derived bracket and a recent work of Lazarev, Sheng, and Tang, we construct an L∞[1]-algebra whose Maurer–Cartan elements are precisely relative Rota–Baxter algebras. By a standard twisting, we define a new L∞[1]-algebra that controls Maurer–Cartan deformations of a relative Rota–Baxter algebra ( A, M, T). We introduce the cohomology of a relative Rota–Baxter algebra ( A, M, T) and study infinitesimal deformations in terms of this cohomology (in low dimensions). As an application, we deduce cohomology of triangular skew-symmetric infinitesimal bialgebras and discuss their infinitesimal deformations. Finally, we define homotopy relative Rota–Baxter operators and find their relationship with homotopy dendriform algebras and homotopy pre-Lie algebras.
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25

Zhang, Yi, Xiaosong Peng та Yuanyuan Zhang. "Typed Angularly Decorated Planar Rooted Trees and Ω-Rota-Baxter Algebras". Mathematics 10, № 2 (2022): 190. http://dx.doi.org/10.3390/math10020190.

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As a generalization of Rota–Baxter algebras, the concept of an Ω-Rota–Baxter could also be regarded as an algebraic abstraction of the integral analysis. In this paper, we introduce the concept of an Ω-dendriform algebra and show the relationship between Ω-Rota–Baxter algebras and Ω-dendriform algebras. Then, we provide a multiplication recursion definition of typed, angularly decorated rooted trees. Finally, we construct the free Ω-Rota–Baxter algebra by typed, angularly decorated rooted trees.
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Nichita, Florin F. "Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems." Axioms 12, no. 4 (2023): 341. http://dx.doi.org/10.3390/axioms12040341.

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This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, E I π+U=O. We refer to a related equation, the Yang–Baxter equation, and to Yang–Baxter systems. The most consistent part of the paper is on the unification of rings and Boolean algebras. These new structures are related to the Yang–Baxter equation and to Yang–Baxter systems.
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Xu, Senrong, Wei Wang, and Jia Zhao. "Twisted Rota-Baxter operators on Hom-Lie algebras." AIMS Mathematics 9, no. 2 (2023): 2619–40. http://dx.doi.org/10.3934/math.2024129.

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<abstract><p>Uchino initiated the investigation of twisted Rota-Baxter operators on associative algebras. Relevant studies have been extensive in recent times. In this paper, we introduce the notion of a twisted Rota-Baxter operator on a Hom-Lie algebra. By utilizing higher derived brackets, we establish an explicit $ L_{\infty} $-algebra whose Maurer-Cartan elements are precisely twisted Rota-Baxter operators on Hom-Lie algebra s. Additionally, we employ Getzler's technique of twisting $ L_\infty $-algebras to establish the cohomology of twisted Rota-Baxter operators. We demonstrate that this cohomology can be regarded as the Chevalley-Eilenberg cohomology of a specific Hom-Lie algebra with coefficients in an appropriate representation. Finally, we study the linear and formal deformations of twisted Rota-Baxter operators by using the cohomology defined above. We also show that the rigidity of a twisted Rota-Baxter operator can be derived from Nijenhuis elements associated with a Hom-Lie algebra.</p></abstract>
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28

Houndedji, Gbevewou Damien, and Cyrille Essossolim Haliya. "Anticenter-Symmetric Bialgebras." Asian Research Journal of Mathematics 21, no. 5 (2025): 76–94. https://doi.org/10.9734/arjom/2025/v21i5926.

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This paper develops a bialgebra theory for anticenter-symmetric algebras by introducing the concept of an anticenter-symmetric bialgebra, equivalent to a Manin triple of anticenter-symmetric algebras. A study of this framework leads to the anticenter-symmetric Yang-Baxter equation in anticenter-symmetric algebras, analogous to the classical Yang-Baxter equation in Mock Lie algebras and the associative Yang-Baxter equation.An unexpected finding is that the anticenter-symmetric and associative Yang-Baxter equations share the same form. Additionally, skew-symmetric solutions to the anticenter-symmetric Yang-Baxter equation define anticenter-symmetric bialgebras. To advance the theory, the paper introduces O-operators and pre-anticentersymmetric algebras, which facilitate the construction of these solutions and provide a foundation for further exploration.
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29

GUO, LI. "BAXTER ALGEBRAS, STIRLING NUMBERS AND PARTITIONS." Journal of Algebra and Its Applications 04, no. 02 (2005): 153–64. http://dx.doi.org/10.1142/s0219498805001083.

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Recent developments of Baxter algebras have led to applications to combinatorics, number theory and mathematical physics. We relate Baxter algebras to Stirling numbers of the first and the second kinds, partitions and multinomial coefficients. This allows us to apply congruences from number theory to obtain congruences in Baxter algebras.
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30

&NA;. "Factor VIII ??? Baxter." Drugs in R & D 4, no. 6 (2003): 366–68. http://dx.doi.org/10.2165/00126839-200304060-00007.

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31

Fee, Elizabeth, Theodore M. Brown, Jan Lazarus, and Paul Theerman. "Baxter Street Then." American Journal of Public Health 92, no. 5 (2002): 753. http://dx.doi.org/10.2105/ajph.92.5.753.

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32

Hodson, Hal. "Baxter breaks out." New Scientist 223, no. 2979 (2014): 19. http://dx.doi.org/10.1016/s0262-4079(14)61434-2.

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33

Lechevalier, Dominique, Lisa Bialé, Camille Glanowski, Isabelle Imbert, Evelyne Péroux, and Frédéric Banal. "Syndrome de Baxter." Revue du Rhumatisme 83, no. 3 (2016): 233. http://dx.doi.org/10.1016/j.rhum.2015.11.009.

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34

Marais, Ben J., Ronald Van Toorn, Tony Figaji, and Guy E. Thwaites. "Reply to Baxter." Clinical Infectious Diseases 69, no. 4 (2019): 736. http://dx.doi.org/10.1093/cid/ciz026.

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35

Bray, Garth M., and Joseph B. Martin. "Donald W. Baxter." Annals of Neurology 73, no. 6 (2013): 685. http://dx.doi.org/10.1002/ana.23912.

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36

Guo, Qiaoling, Ling Liu, Jiafeng Lü, Bingliang Shen, and Xingting Wang. "Rota-Baxter Systems for BiHom-Type Algebras." Mathematics 10, no. 18 (2022): 3222. http://dx.doi.org/10.3390/math10183222.

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The purpose of this paper is to study Rota–Baxter systems for BiHom-type algebras such as BiHom analogues of associative, dendriform, quadri algebras. It is shown that BiHom-dendriform structures of a particular kind are equivalent to Rota–Baxter systems. It is shown further that a Rota–Baxter system induces a weak BiHom-pseudotwistor which can be held responsible for the existence of a new product on the underlying BiHom-associative algebra. Moreover, we study the relationship between BiHom-quadri-algebras and Rota–Baxter systems for BiHom-dendriform algebras.
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37

Guo, Shuangjian, Shengxiang Wang, and Xiaohui Zhang. "The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras." Mathematics 10, no. 11 (2022): 1920. http://dx.doi.org/10.3390/math10111920.

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In this paper, we first introduce the notion of Hom–Leibniz bialgebras, which is equivalent to matched pairs of Hom–Leibniz algebras and Manin triples of Hom–Leibniz algebras. Additionally, we extend the notion of relative Rota–Baxter operators to Hom–Leibniz algebras and prove that there is a Hom–pre-Leibniz algebra structure on Hom–Leibniz algebras that have a relative Rota–Baxter operator. Finally, we study the classical Hom–Leibniz Yang–Baxter equation on Hom–Leibniz algebras and present its connection with the relative Rota–Baxter operator.
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38

Wang, Zhongwei, Zhen Guan, Yi Zhang, and Liangyun Zhang. "Rota–Baxter Operators on Cocommutative Weak Hopf Algebras." Mathematics 10, no. 1 (2021): 95. http://dx.doi.org/10.3390/math10010095.

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In this paper, we first introduce the concept of a Rota–Baxter operator on a cocommutative weak Hopf algebra H and give some examples. We then construct Rota–Baxter operators from the normalized integral, antipode, and target map of H. Moreover, we construct a new multiplication “∗” and an antipode SB from a Rota–Baxter operator B on H such that HB=(H,∗,η,Δ,ε,SB) becomes a new weak Hopf algebra. Finally, all Rota–Baxter operators on a weak Hopf algebra of a matrix algebra are given.
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39

Iantovics, Laszlo Barna, and Florin Felix Nichita. "On the Colored and the Set-Theoretical Yang–Baxter Equations." Axioms 10, no. 3 (2021): 146. http://dx.doi.org/10.3390/axioms10030146.

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This paper is related to several articles published in AXIOMS, SCI, etc. The main concepts of the current paper are the colored Yang–Baxter equation and the set-theoretical Yang–Baxter equation. The Euler formula, colagebra structures, and means play an important role in our study. We show that some new solutions for a certain system of equations lead to colored Yang–Baxter operators, which are related to an Euler formula for matrices, and the set-theoretical solutions to the Yang–Baxter equation are related to means. A new coalgebra is obtained and studied.
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40

Zhang, Chengwei, Zhongmin Liu, Zezhao Lu, and Donghai Ma. "Experiment of droplet contact angle hysteresis on PTFE fibrous membrane in pore-scale." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, February 12, 2024. http://dx.doi.org/10.1177/09544062241231407.

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The present paper aims to study the influence of pore-scale fiber structure on the Cassie-Baxter contact angle of droplets on PTFE fibrous hydrophobic membranes. The fiber structure is obtained by the Confocal Laser Scanning Microscope (CLSM), and an optical test bench is built to measure the Cassie-Baxter contact angles of a droplet on a PTFE membrane. The free energy of the solid-liquid interface is measured by the surface tension integral on the droplet profile. An iterative algorithm for liquid-vapor interface shrinking is brought forward to analyze the liquid-vapor interface area between the droplet and the membrane, and the interface parameters of the Cassie-Baxter model are recognized. The experiment shows that the Cassie-Baxter contact angles and the contact line radii along the droplet circumference are in a normal distribution due to random fiber structures, and the variance of the normal distribution increases with the membrane pore diameter. The normal distribution of Cassie-Baxter’s contact angle indicates the constraint of the solid-liquid interface to the liquid-vapor interface. On the same normal contact pressure condition, the liquid-vapor area ratio of the droplet and membrane interface changes little, and Cassie-Baxter’s contact angle increases with the solid-liquid interface area ratio.
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41

"Baxter." Analytical Chemistry 59, no. 17 (1987): 984A. http://dx.doi.org/10.1021/ac00144a702.

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"Baxter." Analytical Chemistry 59, no. 21 (1987): 1220A. http://dx.doi.org/10.1021/ac00148a702.

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"Baxter." Analytical Chemistry 60, no. 19 (1988): 1080A. http://dx.doi.org/10.1021/ac00170a711.

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"Baxter." Analytical Chemistry 60, no. 19 (1988): 1082A. http://dx.doi.org/10.1021/ac00170a715.

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"Baxter." Analytical Chemistry 60, no. 21 (1988): 1189A. http://dx.doi.org/10.1021/ac00172a708.

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"Baxter." Analytical Chemistry 60, no. 21 (1988): 1192A. http://dx.doi.org/10.1021/ac00172a711.

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"Baxter." Analytical Chemistry 60, no. 23 (1988): 1314A. http://dx.doi.org/10.1021/ac00174a708.

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"Baxter." Analytical Chemistry 60, no. 23 (1988): 1329A. http://dx.doi.org/10.1021/ac00174a724.

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"Baxter." Analytical Chemistry 60, no. 24 (1988): 1374A. http://dx.doi.org/10.1021/ac00175a706.

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"Baxter." Analytical Chemistry 61, no. 3 (1989): 127A. http://dx.doi.org/10.1021/ac00178a708.

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